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Kinetic energy, planetary mases, Bernoulli's Principle

1.A space vehicle returning to Earth is fist slowed by its motors to a speed of 450m/s and then is slowed further to 100m/s by air resistance in the atmosphere. Its average heat capacity is 0.60kJ/kg-Cdegrees. Find the increase in its temperature on the assumption that 70% of the heat produced is absorbed by the vehicle and that it is distributed uniformly through vehicle.

2.A downhill skier of mass 80kg arrives at the last 500m stretch of his run after a big turn which slows him to 22m/s. The remaining slope is at 25 deg. Given that the friction coefficient between his skis and the snow is 0.14, and assuming that all the energy lost due to friction is used to melt the snow sticking to the skis(at 0degrees C), how much snow is melted during this part of the run?

3.In the old Wild Wild West, Dr. Lovelace builds his latest mechanical contraption to try and destroy President Grant's private train with him and his agents inside. The train is planned to pass 77m away from a flat mesa, 144m high, and 44m across. Lovelace is building a frictionless slide at the farthest end of the top of the mesa. From the top of the slide he plans to roll a shperical bomb, which will then roll across the mesa having friction coefficient of 0.007, then freefall, and land right on top of the train, exploding on impact. What is the height of the top of the slide above the mesa top in order for this to be successful?

4.An airliner lands with a speed of 50m/s. Each wheel on the plane has a radius of 1.25m and moment of inertia of 110kgm^2. At touchdown the wheels begin to spin under the action of friction. Each wheel supports a weight of 1.4*10^4N and the wheels attain the angular speed of rolling without slipping in 0.48s. What is the coefficient of kinetic friction between the wheels and the runway? Assume speed of airplane is constant.

5.A flying wing of cross-sectional area 1100sq.meters and mass 220,000kg is level at Sea Level. The engines are producing 214,000N of thrust and the air resistance is 155,000N. When the thrust is applied, the air flows over the wing at 314m/s and below it at 294m/s. What vertical acceleration is experienced at this moment, so that the appropiate compensating trim may be applied?

6.Planet Jovus has a moon which circles it every 31 days in an orbit of radius 7.7*10^8meters, and the planet circles the star Eta-Psi every 7 years in an orbit of 5.5AU. From these figures Newton was able to find the ratio of the masses of our Sun and Earth without knowing the value of G. Do the same and find the ratio of the masses of Jovus and Eta-Psi. Again you cannot use the value of G.

Solution Preview

g= acceleration due to gravity=9.81m/s^2
1.A space vehicle returning to Earth is fist slowed by its motors to a speed of 450m/s and then is slowed further to 100m/s by air resistance in the atmosphere. Its average heat capacity is 0.60kJ/kg-Cdegrees. Find the increase in its temperature on the assumption that 70% of the heat produced is absorbed by the vehicle and that it is distributed uniformly through vehicle.

Change in KE= =1/2(m)(V1^2-V2^2)
= 96250 m
Change in temperature = (T2-T1)

m*s*(T2-T1)= Change in KE*70% ( as specified in the problem)
s=600 J/Kg-c

Cancelling m from both sides of the equation
0.7*96250=600*(T2-T1)

(T2-T1)= 112.29 deg C Answer
2.A downhill skier of mass 80kg arrives at the last 500m stretch of his run after a big turn which slows him to 22m/s. The remaining slope is at 25 deg. Given that the friction coefficient between his skis and the snow is 0.14, and assuming that all the energy lost due to friction is used to melt the snow sticking to the skis(at 0degrees C), how much snow is melted during this part of the run?
M= 80 Kg
X= 500 m
Mu = 0.14
phi= 25 deg
Cos ...

Solution Summary

Answers questions on Kinetic energy, planetary mases, Bernoulli's Principle.

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